This note contains complementary information to the paper Staudigl and Steg
(2014). We present a martingale characterization of continuation payoff processes in a
class of repeated games with imperfect public monitoring. Our martingale approach
allows us to work out a clear connection between the discrete time and continuous
time payoff processes. A general proof of convergence is the open issue in this literature,
and I strongly belief that the characterization result reported here is the key to
solve this problem.